Question

what is the volume of a sphere with a radius of 12 units?
a. 144π units³
b. 2304π units³
c. 576π units³
d. 1728π units³

Explanation:

Step1: Recall volume formula

The volume formula of a sphere is $V = \frac{4}{3}\pi r^{3}$, where $r$ is the radius.

Step2: Substitute radius value

Given $r = 12$, substitute it into the formula: $V=\frac{4}{3}\pi\times(12)^{3}$.

Step3: Calculate $(12)^{3}$

$(12)^{3}=12\times12\times12 = 1728$.

Step4: Calculate volume

$V=\frac{4}{3}\pi\times1728$. $\frac{4}{3}\times1728 = 4\times576=2304$. So $V = 2304\pi$ units$^{3}$.

Answer:

B. $2304\pi$ units$^{3}$